Total positivity of the cubic trigonometric Bézier basis
Summary: Within the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric Bézier basis with two shape parameters \(\lambda\) and \(\mu\) given in [the first author et al., Appl. Math. Lett. 22, No. 2, 226--231 (2009; Zbl 1163.65307)] forms an optimal normalized totally positive basis for \(\lambda,\mu\in(-2,1]\). Moreover, we show that for \(\lambda=-2\) or \(\mu=-2\) the basis is not suited for curve design from the blossom point of view. In order to compute the corresponding cubic trigonometric Bézier curves stably and efficiently, we also develop a new corner cutting algorithm.
scientific article; zbMATH DE number 7010568